In order to determine if two triangles are similar or not we need to check that they satisfy the conditions above. However, there are a few basic principles which allow us to determine whether two triangles are similar without having to measure and compare all their sides and all their angles. These principles are known as cases of similarity in triangles or, criteria of similar triangles.

Use this triangle as a starting point and make similar triangles by dragging point C or by playing around with the scale values. Note that the angles remain equal, whatever the size of the triangle is.

Look carefully at the following window. There are two triangles which are positioned in a special way. Mathematicians often refer to triangles like these as being in Thales' position, in honour of the Greek Mathematician Thales of Miletus.

Now compare the bigger triangle, BDE, with the smaller one inside it, ABC. Work out the value of each angle and write the answers in your exercise book. Are each pair of corresponding angles equal?

A =	E =
B =	B =
C =	D =

If two triangles have two corresponding angles which are equal to each other what can we say about the third angle? Are the two triangles similar? Why?